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Treatments of Fractures Intersection in the Enriched-Embedded Discrete Fracture Model (nEDFM) for Porous Flow

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1 State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
2 School of Mechanical Engineering, Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development, Beijing Institute of Petrochemical Technology, Beijing, 102617, China

* Corresponding Author: Dongxu Han. Email:

The International Conference on Computational & Experimental Engineering and Sciences 2024, 30(1), 1-3. https://doi.org/10.32604/icces.2024.011520

Abstract

Motivated by the fractures being very thin compared to the size of rock matrix, utilizing the non-conforming grid is an efficient approach to simulate fluid flow in fractured porous media. The embedded discrete fracture model (EDFM) is the typical one that using the conforming grid and modelled based on the finite volume method (FVM) framework. The EDFM maintains advantages of mass conservation and low computational complexity, but it cannot characterize blocking fractures and has a low accuracy on the mass exchange between fractures and matrix [1]. In our previous work [2], we developed the enriched-EDFM (nEDFM) to address the two limitations of the classical EDFM. The main feature of the nEDFM is the approximation of pressure distribution inside interaction regions by the local shape function, which introduces two enriched degrees of freedoms (DOF) for each fracture cell and can depict the discontinuities of pressure and its gradient across blocking fractures. However, the original local shape function only applies to the configuration that no more than one fracture line crosses a matrix cell. The function format and the related number of enriched DOF should be modified to handle the more complex discontinuities inside matrix cells crossed by more than one fracture line. This study develops the treatments for matrix cells crossed by two fracture lines, include the situations where fracture lines intersect or do not intersect with each other inside the cell. Five configurations are divided to cover all situations about the fractures distribution inside one cell, and customized local shape functions are proposed for each configuration. Furthermore, the treatment of flow interaction between two fracture lines is also developed to fit the situation that the permeabilities of two fractures have a large difference. The comparison results of a classical case [3] show that the nEDFM still has a high efficiency and accuracy for the case with fractures intersections and has a better performance than the EDFM, projected-EDFM, and extended finite element method (XFEM).

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